QUANTUM COMPUTING - EXAMPLE 32.2 : (a) If | 001 > = | 1 >, | 111 > = | 7 >, find the 2 possible values of ( | 001 > + | 1 > + | 7 > ) ( | 111 > ). (b) In quantum money, a duplicate will have probability P of passing the verification test of a bank, if the total number of photons on the bank note is N. The would be counterfeiter has a probability p of success in duplicating the quantum money correctly for each photon. Guess the relationship of P, p and N as a mathematical formula involving natural logarithm ln.
QUANTUM COMPUTING - ANSWER 32.2 : (a) First answer : ( | 001 > + | 1 > + | 7 > ) ( | 111 > ) = ( | 1 > + | 1 > + | 7 > ) ( | 111 > ) = ( | 9 > ) ( | 111 > ) = | 999 >. Second answer : ( | 001 > + | 1 > + | 7 > ) ( | 111 > ) = ( | 1 > + | 1 > + | 7 > ) ( | 7 > ) = ( | 9 > ) ( | 7 > ) = | 63 >. (b) If N = 1, then P = p. If N = 2, then P = p power 2. If N = 3, then P = p power 3. For N, P = p power N, ln P = ln (p power N), then ln P = N ln p. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 39 - Acetone and ethanol are separated using a distillation column with a partial condenser and partial reboiler. An equimolar, sub-cooled liquid feed enters at 100 kmol / hr and condenses 1 mole of vapor for every 6 moles of feed. The separation requires a distillate vapor that is 95 mol % acetone and bottoms liquid that is 5 mol % acetone. The reflux is returned from the condenser to the column as a saturated liquid and the operation is run at (L / V) = 1.4 * (L / V) min. Assume constant overflow conditions. (a) Feed operating line is y = [ q / (q - 1) ] x - z / (q - 1) where z = 0.5 for equimolar liquid mixture of 2 components, q = (L’ - L) / F where L’ = L + F + (F / 6) for condensation of 1 mole of vapor / 6 moles of feed. What is y = f(x)? (b) The rectifying operating line is y = (L / V) x + (D / V) (xd) where (L / V) min goes through the points A (0.95, 0.95) and B (0.53, 0.69), V = L + D. What is y = f(x)? Let xd = 0.95. (L / V) min is the slope of the 2 points A and B.
Question 51 - A batch reactor is designed for the system of the irreversible, elementary liquid-phase hydration of butylene oxide that produces butylene glycol. At the reaction temperature T = 323 K, the reaction rate constant is k = 0.00083 L / (mol - min). The initial concentration of butylene oxide is 0.25 mol / L = Ca. The reaction is conducted using water as the solvent, so that water is in large excess. (a) Let the molecular weight of water is 18 g / mol and the mass of 1 kg in 1 L of water, calculate the molar density of water, Cb in the unit of mol / L. (b) Determine the final conversion, X of butylene oxide in the batch reactor after t = 45 min of reaction time. Use the formula X = 1 - 1 / exp [ kt (Cb) ] derived from material balance. (c) Find the equation of t as a function of X.
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CHEMICAL FLUID MECHANIC - EXAMPLE 3.3 : The drag coefficient Cd = 0.05 and lift coefficient Cl = 0.4 for a levelled flow aircraft are measured. The velocity of the aircraft is v = 150 ft / s with its weight W = 2677.5 pound-force. (a) Find the value of the lift of the aircraft, L, when it is also its weight. (b) The drag of the aircraft, D = Cd M, L = Cl M. Find the value of D. (c) The power required is P = Dv. If 1 pound-force x (ft / s) = 1.356 W, find the value of P in the unit of Watt or W.
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